Final answer:
The capacitive reactance of a 500 pF capacitor in a circuit with a frequency of 100 kHz is approximately 3183.1 ohms. The total capacitance of the circuit with capacitors of 5 F, 12 MF, and 22 uF is approximately 12,000,027 F. The current in the circuit connected to a 208-volt, 60 Hz power line is approximately 0.0653 A or 65.3 mA.
Step-by-step explanation:
The capacitive reactance of a capacitor can be calculated using the formula XC = 1 / (2πfC), where XC is the capacitive reactance, f is the frequency, and C is the capacitance. In this case, the frequency is 100 kHz and the capacitance is 500 pF (or 500 * 10-12 F), therefore:
XC = 1 / (2π * 100,000 * 500 * 10-12)
XC ≈ 3183.1 ohms
To find the total capacitance of capacitors connected in parallel, you simply add up their capacitances. In this case, the total capacitance of the circuit with capacitors of 5 F, 12 MF, and 22 uF would be:
Total capacitance = 5 F + 12 * 106 F + 22 * 10-6 F
Total capacitance ≈ 12,000,027 F
Finally, to calculate the current in the circuit, you can use Ohm's Law: I = V / XC, where I is the current, V is the voltage, and XC is the capacitive reactance. Since the voltage is 208 volts and the capacitive reactance is 3183.1 ohms, therefore:
I = 208 / 3183.1
I ≈ 0.0653 A or 65.3 mA